How many distinct primitive roots are there modulo 81? Hc modulo 162?

Q: Find the degree and leading coefficient for the given polynomial. Degree: Number Leading Number…

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Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .

Q: 5. 2e* cot y dx - (4 + e*) csc²y dy = 0

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Q: Determine the coordinates of the vertices of the following quilt pattern if the bottom left-hand…

A: Here we found the length of sides of square IJPO and the whole square ADXU(given). We also found the…

Q: Consider the following series. n=1 lim n→ ∞ Use the Limit Comparison Test to complete the 7 gn +1 7…

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Q: Calculate f f (x, y, z) ds for the given surface and function. (r, 0) (r cos (0), r sin (0), 0),…

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Q: Calculate the Fourier sine series expansion of g(x) = ²7³ on [0, π].

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Q: Let F(x, y) = ²+y² • (x,y) (a) Compute V × F. In what open, connected region D can you conclude that…

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Q: Sketch the curve. r = 3 - sin(8)

A: It can be easily done by using graphing tools

Q: Evaluate the the integral ff, (x²+y+z)dS where S is the portion of the plane z = x + 3 that lies…

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Q: Determine {F}. F(s) = 6s² +96s+328 (S-2) (s² + 12s +40) Click here to view the table of Laplace…

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Q: Find the first four nonzero terms of the Fourier cosine series of f. f(t)= Find the first four…

A: A function f(t) defined on an interval 0 < t < L is given.Find the Fourier cosine and sine…

Q: 12. Find the surface are of the object obtained by rotating x = e²y, -1 ≤ y ≤ 0

A: 12. Given,                 To find the surface area of the object obtained by rotating      'x'…

Q: a) i. Let M and 4 be any two numbers of the form 42+1 ii. Let Mand N be any off the form 4r +3 Prove…

A: Since you have posted multiple questions, we will answer the first question for you. If you want any…

Q: Find the volume of the largest box of the type shown in the figure, with one corner at the origin…

A: solution :

Q: The discrete Fourier transform (DFT) of a periodic array f₁, for j = 0, 1,..., N - 1 (corresponding…

A: Solution (a)

Q: I need help with this problem becuase I don't know

A: GivenGradient of  is

Q: Prove that the set of numbers Q(√2) = { a+b√2: a, b = Q} is a field.

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Q: o points, A and B, are on opposite sides of a building..

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Q: 1. Prove that the system 1 ¹+x (² - x² - y²), * = -x + y (¹-x² - y²) 2 x = y + x has a stable limit…

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Q: Suppose you have a set of integers from 1 to 20 (inclusive). How many subsets can you form from this…

A: A set in mathematics is a collection of distinct objects, considered as an object in its own…

Q: Let T(x, y) = 10 + 5x² + y be a temperature function on a metallic plate. Find the maximum value of…

A: Given the temperature function is                                              and…

Q: 1. Let a be an element of a ring R. Let S = {x €= R | ax = 0}. Show that S is a subring of R. Show…

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Q: and the total outside surface area and volume of the solid object. Assume at the base is regular. 30…

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Q: 15. convergence. b. Find a power series for the function, centered at 0, and determine the interval…

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Q: 1-2 0-4 5 0 0 0 13 -2 0 3 5 Let A = 0 1 a. Find a basis for Col A and find Rank A. b. Find a basis…

A: The given matrix,The objective is to find,(a) Basis for and rank of .(b) Basis for .

Q: Сав (аль) =ажь b = ⇒ inverse of (a*b) = axb. (ахь) = ажь) П

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Q: use properties of power series, substitution, and factoring to find the first four nonzero terms of…

A: The given function .The objective is to find the Taylor series of the function centered at .

Q: Find the Z(cos 3n + 2) and Z(n5").

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Q: Convergent Series Sum Illustrate with an example that a convergent series ek need not have the sum…

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Q: Evaluate sin sin(x) dx + z cos(y) dy + sin(y) dz where C is the elipse 25x² + 16y2 = 49, oriented…

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Q: For what values of p is each series convergent? Op # -3 Op>0 Op> -3 for all P Op≥-3 ES n=1 (-1)^-1…

A: We have to find the value of .

Q: A baseball player hits the ball and then runs down the first base line at 17 ft/s. The first baseman…

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Q: Determine the interval and radius of convergence of (-1)^8¹+n n+4 n=0 -(x-7)"

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Q: Sketch the following parametric curves on your work sheet. Attach the photos to this question. 4…

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Q: could you solve for the part D and i think they made a mistake for value a and b, the corrent value…

A: We can observe from the research above that a good's value is always declining over time. V(t)…

Q: Find the solution of the initial value problem (2y2 +1-xy) dy-y² dx = 0, y(2) = 1.

A: The given initial value problem .The aim is to solve the initial value problem.

Q: Prove by induction Bernoulli’s Identity: For every real number x > −1 and every positive integer n,…

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Q: A property expected from Grothedieck universe U is to be closed under the usual operations with…

A: A Grothendieck universe U is a set that satisfies certain properties that make it useful for the…

Q: Consider the vector space R^n with inner product

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Q: Solve the system of differential equations. [6 -2] [2 13] T 2 10 x'= x₁ (0) = 14, x₂(0) = 26 X T₁(t)…

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Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 11 tan ¹(²); P(-12,12);…

A: Let        we can find directional derivatives of given function f(x,y)

Q: maximize Subject to Z= 50x₁ +80x₂ +64x3 + 80x4 5x₁2.5x₂ + 4.5x3 +3.99x4 ≤ 600 4.1x₁ + 2.6x₂ +5.5x3…

A: Transform the problem into standard form

Q: Identify R²+¹ with the set Pn of polynomials of degree ≤n, via the corre- spondence (an, ao) → ant +…

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Q: 2.6 Apply the inverse-transform method to generate random variables from a Laplace distribution…

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Q: Question 2. Ifø is a normalized fundamental matrix X = AX at to = 0 and if F is continuous in t,…

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Q: A vector field F and contour lines of a potential function for F are shown in the figure. Já 17 F.…

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Q: 9 practice problem Evaluate the surface integral 2m F(x, y, z) = -xi-yj + z³k, S is the part of the…

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Q: Use the information given in the figure below to construct a mathematical model for the number of…

A: Given,

Q: Consider a parametrization of a standard cylinder in R³ (a) Verify J¹ J = 1 0 0 0²0 0 1 0 r(r, 0, z)…

A: (a). Given that a parametrization of a standard cylinder in R3 given by…